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Regular and Chaotic Dynamics, 2008, Volume 13, Issue 6, Pages 543–556
DOI: https://doi.org/10.1134/S1560354708060051 (Mi rcd600) 		 
This article is cited in 25 scientific papers (total in 25 papers)

JÜRGEN MOSER – 80

Integrable Lotka–Volterra systems

O.I. Bogoyavlenskijab

a V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b Department of Mathematics, Queen’s University, Kingston, K7L 3N6, Canada
Citations (25)
DOI: https://doi.org/10.1134/S1560354708060051
Abstract: Infinite- and finite-dimensional lattices of Lotka–Volterra type are derived that possess Lax representations and have large families of first integrals. The obtained systems are Hamiltonian and contain perturbations of Volterra lattice. Examples of Liouville-integrable 4-dimensional Hamiltonian Lotka-Volterra systems are presented. Several 5-dimensional Lotka–Volterra systems are found that have Lax representations and are Liouville-integrable on constant levels of Casimir functions.
Keywords: Lax representation, Hamiltonian structures, Casimir functions, Riemannian surfaces, Lotka–Volterra systems, integrable lattices.
Received: 06.09.2008
Accepted: 28.10.2008
Bibliographic databases:
Document Type: Personalia
MSC: 58F05
Language: English
Citation: O.I. Bogoyavlenskij, “Integrable Lotka–Volterra systems”, Regul. Chaotic Dyn., 13:6 (2008), 543–556
Citation in format AMSBIB
\Bibitem{Bog08}
\by O.I. Bogoyavlenskij
\paper Integrable Lotka–Volterra systems
\jour Regul. Chaotic Dyn.
\yr 2008
\vol 13
\issue 6
\pages 543--556
\mathnet{http://mi.mathnet.ru/rcd600}
\crossref{https://doi.org/10.1134/S1560354708060051}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2465723}
\zmath{https://zbmath.org/?q=an:1229.37097}
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    • This publication is cited in the following 25 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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